y ) ∈ Y with y ≠ 0 has a preimage. Hence for any subvariety W = V ( I W ) ⊂ X ⊂ P d Σ there exists W ′ ⊂ Y ⊂ P d + s − 1 Σ ,X such that π ( W ′ ) = W , i.e., W ′ = { z = ( x, y ) ∣ x ∈ W } .\n\nFor X ⊂ P d Σ a quasi-smooth intersection variety the morphism in cohomology induced by the inclusion i ∗ ∶ H d − s ( P d Σ , C ) → H d − s ( X, C ) is injective by Proposition 1.4 in [7].\n\nDeﬁnition 4.2. The primitive cohomology of H d − s prim ( X ) is the quotient H d − s ( X, C )/ i ∗ ( H d − s ( P d Σ , C )) and H d − s prim ( X, Q ) with rational